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Okay, we're now going to look graphically at the labor leisure choice problem. I've
got my two goods. On the horizontal axis is leisure and on the vertical axis is consumption.
I am assuming that the time endowment is 24 and when there's no wage income... this corner
point on the budget line is 24,0. And the only variable that you get to select is the
wage. So let's watch what happens when I raise the wage to the other axis. And just look
at the axis for the moment don't worry about the point here. Raising the wage allows you
to have more consumption. If you were to take all that leisure time and work with it. And
likewise lowering the wage lowers this intercept. So this is zero leisure and the wage times
24 dollars worth of consumption. So that's budget line is given by this blue line.
I have three indifference curves here. Here's a low one. Here's a high one in purple. And
the red one is the one that's tangent to the budget line at the optimal point. This dashed
line here is the price consumption curve as I vary the wage or as I lower the price of
consumption. And what you'll notice here is that that price consumption curve has an odd
shape.
So let's make the wage very low for a second. Let's lower it. And at very low wages as I
raise the wage I have less leisure more consumption. So as I raise the wage I have more labor supply.
Eventually however I reach a point where I'm actually having a lot of labor supply and
not much leisure. And then thereafter the curve bends the other way. And then what one
gets actually is that labor supply starts to decline in the wage at higher wages. This
is perfectly okay. This is what's happening because this is a cross price effect. That
is the raise in the wage is really just a fall in the price of consumption. And the
effect on leisure can go either way depending on whether consumption demand is elastic or
inelastic.
Let's now move to look at the same picture but now we're in labor supply space. So here
we have the hourly wage on this axis. And here we have labor supply. Again let me lower
the wage. And as long as it's lower than this amount further lowering of the wage reduces
labor supply. So labor supply slopes up at low wages, which is sensible. But you reach
this wage, around $6.40 I think, and then thereafter if you raise the wage actually
labor supply is being reduced.
We call this backward bending labor supply here. I shouldn't have done that. And backward
bending labor supply happens again because raise the wage is really lowering the price
consumption. And the question again is whether is consumption elastic or inelastic in its
demand?Okay, that's all there is to it.